Simplification and analysis of models of calcium dynamics based on IP3-sensitive calcium channel kinetics (original) (raw)

1996, Biophysical Journal

We study the models for calcium (Ca) dynamics developed in earlier studies, in each of which the key component is the kinetics of intracellular inositol-1,4,5-trisphosphate-sensitive Ca channels. After rapidly equilibrating steps are eliminated, the channel kinetics in these models are represented by a single differential equation that is linear in the state of the channel. In the reduced kinetic model, the graph of the steady-state fraction of conducting channels as a function of log1O(Ca) is a bell-shaped curve. Dynamically, a step increase in inositol-1,4,5-trisphosphate induces an incremental increase in the fraction of conducting channels, whereas a step increase in Ca can either potentiate or inhibit channel activation, depending on the Ca level before and after the increase. The relationships among these models are discussed, and experimental tests to distinguish between them are given. Under certain conditions the models for intracellular calcium dynamics are reduced to the singular perturbed form edx/dT = f(x, y, p), dy/dT = g(x, y, p). Phase-plane analysis is applied to a generic form of these simplified models to show how different types of Ca response, such as excitability, oscillations, and a sustained elevation of Ca, can arise. The generic model can also be used to study frequency encoding of hormonal stimuli, to determine the conditions for stable traveling Ca waves, and to understand the effect of channel properties on the wave speed. Cytoplasmic calcium (Ca,) is a universal second messenger for regulation of many cellular components and processes, including muscle contraction, secretion, membrane permeability, and fertilization. The extracellular signals for such processes can be hormones, growth factors, neurotransmitters, membrane depolarization, or physical signals such as light or shear stresses. One mode of regulation of Ca, is by means of the activation and inactivation of Ca channels between the cytoplasm and intracellular Ca stores, which are either the endoplasmic reticulum (ER) in nonmuscle cells or the sarcoplasmic reticulum (SR) in muscle cells. These channels are of two major types, inositol-1,4,5trisphosphate (lP3)-sensitive Ca channels (IP3R) and ryanodine-sensitive Ca channels (RyR), but there may be many subtypes of these two types, depending on the cell type in question. Experiments in which IP3R are inserted into lipid bilayers show that IP3 upregulates the channel activity (Watras et al., 1991), whereas Ca has both a positive and a negative effect on the channel activity. At steady state the graph of the fraction of channels open versus logl0([Cal]), which we denote pCa, is a bell-shaped curve (Bezprozvanny et al., 1991). Moreover, activation of channels at low Ca concentrations and inhibition at high concentrations are seen in a